Fast Sampling of Diffusion Models for Accelerated MRI using Dual Manifold Constraints

Diffusion models show great potential in solving inverse problems, including MRI reconstruction. With its unique characteristics, medical imaging demands both efficiency and accuracy in the reconstruction process. However, existing MRI reconstruction methods based on diffusion models often fall short of fully leveraging the available measurements during sampling. Consequently, these methods suffer from compromised reconstruction quality and elevated bias, especially when dealing with large acceleration factors. In response to these challenges, we propose Dual Manifold Constraints (DMC), a fast MRI reconstruction method based on diffusion models. We treat the sampling process as a combination of denoising and adding noise processes, and we constrain these two processes using both pristine measurements and their noisy counterparts to adapt to the geometry of diffusion. It's worth noting that we propose a method to estimate the noisy measurement that satisfies the sub-sampling process to maintain the current data manifold when performing data consistency constraints. Experimental results show that our method outperforms the latest diffusion-based methods regarding both reconstruction speed and accuracy, and exhibits strong out-of-distribution generalization performance.